The effects of station density in geostatistical prediction of air temperatures in Sweden: A comparison of two interpolation techniques

Abstract

High fidelity gridded temperature datasets are difficult to obtain for areas with sparse coverage of meteorological stations given that sparsity of stations is known to introduce uncertainty in the interpolation of climatic variables generally. Inspired by their potential for optimal results especially for small sample datasets, the accuracy of interpolation results of Empirical Bayesian Kriging (EBK) and EBK-Regression Prediction (EBKRP) spatial prediction techniques were assessed and compared under varying sampling density scenarios, using monthly maximum temperature normals (1991–2020) for the entire area of Sweden. The objective of the was to understand how EBK and EBKRP interpolation techniques perform in different sampling density scenarios and in a sparse data setting, and the possible difference in the prediction accuracy between the two techniques. The 708 sampled stations obtained from the historical climatology database of the Swedish Meteorological and Hydrological Institute (SMHI) were split into seven sampling density subsets, ranging from 1 sample per 63,614 km 2 to 1 sample per 634,350 km 2 and representing both low and high sampling density scenarios. EBK interpolation technique was implemented using temperature data while land use land cover (LULC) and digital elevation model (DEM) were used as temperature covariates for the EBKRP interpolation models. The prediction accuracy assessment was based on five robust prediction performance indicators - mean error, mean absolute error, mean square error, root mean square error and Pearson correlation (R) - obtained from independent validation/cross-validation operations. Prediction accuracy was found to be generally positively related to sampling density and sampling density accounted for 85%–87% of interpolation accuracy for both EBK and EBKRP techniques. Although sampling density increased linearly, the rate of change in accuracy from one sampling density step to the next was not particularly proportional. A rapid increase in accuracy was observed when transiting from 40% to 60% sampling density scenario, but the rate of change in accuracy remained fairly stable before and after this (40% to 60%) sampling density scenario. For equivalent sampling density set-ups, EBKRP consistently performed better than EBK in all the accuracy metrics and EBKRP proved to be about 40% better than EBK. However, the two interpolation techniques produced generally very low prediction biases at all the sampling density scenarios investigated. Our study suggests that potential effects of low sampling density and non-stationarity of temperature data can be significantly reduced by applying EBK but especially EBKRP when coupled with relevant covariates. We also concluded that EBK and EBKRP can be applied to generate accurate prediction surfaces even in a widely varying sampling density setting including environments with moderately low sample density. This is especially true for continuous and slowly varying phenomena such as temperature and similar variables. • Station density is positively related to interpolation accuracy of air temperature but in non-linear fashion. • Univariate and multivariate Empirical Bayesian Kriging interpolation techniques can produce high prediction accuracy result even when data density is small or locally non-stationary. • Multivariate Empirical Bayesian Kriging technique performs better than the univariate technique in different sampling density settings when predicting air temperature. • Normally distributed data can generally improve prediction results even when data density is relatively small or sparse.